# Spontaneous symmetry breaking and the flat phase of crystalline membranes

## TL;DR

This paper investigates how spontaneous symmetry breaking, influenced by the crystalline lattice, stabilizes the flat phase of crystalline membranes, highlighting the role of Goldstone modes in maintaining long-range order.

## Contribution

It introduces a novel symmetry breaking mechanism linked to the flat phase, emphasizing the lattice's role in long-range order in crystalline membranes.

## Key findings

- Identification of a symmetry breaking mechanism involving Goldstone modes
- Crystalline lattice crucial for stabilizing the flat phase
- Links between symmetry patterns and physical properties of membranes

## Abstract

Crystalline membranes are one of the rare examples of bidimensional systems in which long-range order can stabilise an ordered phase in the thermodynamic limit. By a careful analysis of the Goldstone modes counting, we propose a symmetry breaking mechanism associated with the generation of the flat phase and show how it highlights the crucial role played by the crystalline lattice in the establishment of long-range order in these objects. Comparison with other symmetry breaking mechanisms in membrane physics is also used to unveil the links between symmetry breaking patterns and the physical properties of the flat phase.